"SIGNATURES" OBSERVED IN A WOIRGARD'S TYPE PENDULUM

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”SIGNATURES” OBSERVED IN A WOIRGARD’S TYPE PENDULUM

W. Benoit, A. Rivière, J. Woirgard

To cite this version:

W. Benoit, A. Rivière, J. Woirgard. ”SIGNATURES” OBSERVED IN A WOIRGARD’S TYPE PENDULUM. Journal de Physique Colloques, 1987, 48 (C8), pp.C8-299-C8-304.

�10.1051/jphyscol:1987843�. �jpa-00227147�

JOURNAL DE PHYSIQUE

Colloque C8, supplément au n°12, Tome 48, décembre 1987 C8-299

"SIGNATURES" OBSERVED IN A WOIRGARD'S TYPE PENDULUM

W. BENOIT, A. RIVIERE* and J. WOIRGARD*

Instltut de G6nie Rtomique, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland

*ENSMR, 20 rue Guillaume VII, F-86034 Poitiers Cedex, France

Abstract. The two waves acoustic coupling method has been extensively used to study different relaxation mechanisms due to dislocation motion.

The advantage of the method is that the feature of the so called

"signature" gives information about the mechanism controlling the dislo- cation motion. The disadvantage of the high frequency ultrasonic stress, used to measure the attenuation and the velocity, is that only pure metals can be studied.

In this paper are shown results obtained in a low frequency pendulum (10~5 to 102 Hz) of the Woirgard's type. The two waves acoustic method is employed for studying I.F. peaks in aluminium. In this case the coupling method consists of applying simultaneously a very low frequency torsion stress (10~4 Hz) and to measure the damping using a "high frequency" (20 Hz) torsion stress.

Résumé. On s a i t l ' i n t é r ê t de l a t e c h n i q u e des o n d e s a c o u s t i q u e s c o u p l é e s p o u r l ' é t u d e des phénomènes de r e l a x a t i o n c o r r é l é s à l a m o b i l i t é des d i s l o c a t i o n s . L ' i n t é r ê t de c e t t e t e c h n i q u e e x p é r i m e n t a l e r é s i d e dans l e f a i t que l e s ".signatures" observées donnent des informa- t i o n s s p é c i f i q u e s s u r l e mécanisme c o n t r ô l a n t l a m o b i l i t é des d i s l o c a - t i o n s . T o u t e f o i s , l ' i n c o n v é n i e n t de l a t e c h n i q u e u l t r a s o n o r e h a u t e fréquence (10 MHz) u t i l i s é e pour mesurer l a v i t e s s e e t l ' a t t é n u a t i o n de l ' o n d e a c o u s t i q u e e s t q u ' e l l e ne p e u t ê t r e u t i l i s é e que dans des matériaux p u r s .

Dans c e t a r t i c l e sont p r é s e n t é s des p r e m i e r s r é s u l t a t s obtenus dans un p e n d u l e f o r c é à t r è s b a s s e fréquence (10~

5

Hz à 10

+2

Hz) . La méthode à deux ondes e s t u t i l i s é e pour é t u d i e r des p i c s de f r o t t e m e n t i n t é r i e u r dans l ' a l u m i n i u m . Dans ce c a s , l a méthode c o n s i s t e à déformer en t o r s i o n un é c h a n t i l l o n à t r è s b a s s e f r é q u e n c e (10~

4

Hz) e t à mesurer l ' a t t é n u a t i o n d ' u n e c o n t r a i n t e de t o r s i o n h a u t e fréquence (20 Hz) superposée.

I INTRODUCTION

Important progress in the study of dislocation dynamics has been achieved using a two waves acoustic method, which has been called the coupling technique [1,2]. In this method the attenuation a and the velocity v of ultrasonic waves (~10 MHz) are measured in a sample submitted simultaneously to an harmonic stress a of low frequency (~ 0.1 H z ) . Closed curves Aa/(o)and Av/v(0) are drawn during each cycle of the applied stress. The shapes of these curves and their evolution are characteristic of each dislocation motion mechanism which is activated

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987843

JOURNAL DE PHYSIQUE

by t h e low f r e q u e n c y a p p l i e d s t r e s s . F o r t h i s r e a s o n , t h e c l o s e d c u r v e s Aa(o) a n d A v / v ( o ) h a v e b e e n c a l l e d t h e " s i g n a t u r e s " o f t h e mechanism which c o n t r o l s t h e low f r e q u e n c y d i s l o c a t i o n m o t i o n .

Using t h i s t e c h n i q u e d i f f e r e n t r e l a x a t i o n phenomena have b e e n s t u d i e d i n v e r y p u r e o r l e s s p u r e aluminium. I t h a s b e e n c l e a r l y shown t h a t t o d i f f e r e n t r e l a x a t i o n mechanisms c o r r e s p o n d q u i t e d i f f e r e n t " s i g n a t u r e s " . Moreover t h e a n a l y s i s o f t h i s s i g n a t u r e i s a p o w e r f u l t o o l t o deduce t h e d i s l o c a t i o n m o t i o n mechanism r e s p o n s i b l e f o r t h e low f r e q u e n c y r e l a x a t i o n p h e n o m e n a . B u t i n o r d e r t o g i v e a g o o d a n a l y s i s a n a p p r o p r i a t e i n t e r p r e t a t i o n o f t h e h i g h f r e q u e n c y damping (MHz r a n g e ) i s n e c e s s a r y . Two m o d e l s h a v e b e e n u s e d d e p e n d i n g o n t h e o b s e r v e d mechanisms : t h e s t r i n g model

( a =

14) which a l l o w s t o m e a s u r e t h e e v o l u t i o n o f t h e p o i n t d e f e c t s c l o u d a r o u n d t h e d i s l o c a t i o n s a n d t h e k i n k p a i r f o r m a t i o n i n t h e t e m p e r a t u r e r a n g e of t h e Bordoni r e l a x a t i o n . N e v e r t h e l e s s from a more g e n e r a l p o i n t of view, when new s i g n a t u r e s a r e o b s e r v e d w i t h o u t i d e a s o n t h e m i c r o s c o p i c a l m e c h a n i s m s , a p h e n o m e n o l o g i c a l a p p r o a c h f o r t h e s i g n a t u r e a n a l y s i s i s p o s s i b l e [ 3 , 1 1 . Such a n a p p r o a c h g i v e s c r i t e r i a t o d e t e r m i n e t h e main c h a r a c t e r i s t i c s o f t h e mechanisms and o f t h e o b s t a c l e s from which a n i n t e r p r e t a t i o n of t h e o b s e r v e d s i g n a t u r e s c a n be o u t l i n e d . Such c r i t e r i a c a n be o b t a i n e d by c h a n g i n g t h e d i f f e r e n t p a r a m e t e r s o f t h e low f r e q u e n c y a p p l i e d s t r e s s s u c h a s t h e f r e q u e n c y ( f r e q u e n c y i n d e p e n d e n t o r d e p e n d e n t mechanism) o r t h e s t r e s s a m p l i t u d e r a n g e ( s e c t i l e o r t r a n s l a t i v e s i g n a t u r e [ 3 , 1 ] ) and b y c h a n g i n g t h e t e m p e r a t u r e o r b y o b s e r v i n g t h e e v o l u t i o n o f t h e s i g n a t u r e a s a f u n c t i o n o f t i m e (number o f c y c l e s ) .

N e v e r t h e l e s s , due t o t h e u s e of u l t r a s o n i c waves, t h i s method i s s t i l l l i m i t e d i n i t s a p p l i c a t i o n s . E f f e c t i v e l y t h e a t t e n u a t i o n o r v e l o c i t y c h a n g e s o f s u c h waves a r e o n l y s u i t a b l e t o b e i n t e r p r e t e d i n a v e r y p u r e m a t e r i a l . But i n p r i n c i p l e , t h e c o u p l i n g method a n d t h e s i g n a t u r e c o n c e p t c o u l d b e u s e d i n q u i t e d i f f e r e n t f r e q u e n c y r a n g e . The g o a l of t h i s p a p e r i s t o show f i r s t r e s u l t s o b t a i n e d i n a low f r e q u e n c y pendulum t o Hz) o f W o i r g a r d ' s t y p e [ 4 ] . I n t h i s c a s e , t h e c o u p l i n g method c o n s i s t s o f a p p l y i n g s i m u l t a n e o u s l y a v e r y low f r e q u e n c y t o r s i o n s t r e s s H Z ) a n d t o m e a s u r e t h e damping u s i n g a s u p e r p o s e d h i g h f r e q u e n c y (20 Hz) t o r s i o n s t r e s s .

I1 EXPERIMENTAL PROCEDURE

An h i g h p u r i t y p o l y c r y s t a l l i n e aluminium s a m p l e (64 x 6 x 1 mm3) r o l l e d and a n n e a l e d a t 720 K was u s e d f o r i n t e r n a l f r i c t i o n e x p e r i m e n t s . The a v e r a g e g r a i n d i a m e t e r was 1 mm.

Measurements were made a t s t a b i l i z e d t e m p e r a t u r e (300

-

700 K ) u s i n g an e v a c u a t e d f o r c e d t o r s i o n pendulum.

A t e a c h t e m p e r a t u r e , i n t e r n a l f r i c t i o n was measured a t low ( 2 . 5 x

l o d 6 )

a n d h i g h ( 2 5 x

l o d 6 )

s t r a i n a m p l i t u d e s , i n a l a r g e f r e q u e n c y r a n g e (10-4 Hz - 10 H z ) .

D u r i n g "two waves" e x p e r i m e n t s , t h e d r i v i n g c o i l s w e r e f e d w i t h a l t e r n a t i n g c u r r e n t s from two d i f f e r e n t s o u r c e s :

-

a l a r g e a m p l i t u d e ( c o r r e s p o n d i n g t o a s t r a i n a m p l i t u d e o f 25 10,-6) a n d low f r e q u e n c y Hz

-

10-3 Hz) s i g n a l d e l i v e r e d b y a n e x t e r n a l s i g n a l g e n e r a t o r ,

-

a low a m p l i t u d e ( 2 . 5 x h i g h f r e q u e n c y ( 1 5 Hz) s i g n a l d e l i v e r e d by t h e p r e v i o u s l y d e s c r i b e d a r r a n g e m e n t [ 4 1 .

I n t e r n a l f r i c t i o n was t h e n measured a f t e r e a c h h i g h f r e q u e n c y c y c l e a f t e r c o r r e c t i n g t h e i n f l u e n c e of t h e s l o w l y v a r y i n g low f r e q u e n c y s i g n a l . Mean v a l u e s a f t e r 10, 50 o r 100 h i g h f r e q u e n c y c y c l e s were recorded depending on t h e low frequency u s e d .

I11 EXPERIMENTAL RESULTS

F i g . 1 shows t h e f r e q u e n c y s p e c t r a o b t a i n e d a t t h r e e d i f f e r e n t t e m p e r a t u r e s (491 K, 529 K and 633 K ) and two d i f f e r e n t a m p l i t u d e s of v i b r a t i o n ( 2 . 5 e t 25.10-6). The observed r e l a x a t i o n peak corresponds t o t h e K e peak [ 5 ] o r t h e complex P2 and P j s t u d i e d by R i v i e r e [ 6 ] . The r e l a x a t i o n p a r a m e t e r s can be g o t from t h e p l o t of f i g . 2 . The number on t h i s f i g u r e c o r r e s p o n d s t o t h e o r d e r of t h e measurements. These p o i n t s a r e not a l i g n e d and q u i t e d i f f e r e n t r e l a x a t i o n e n e r g i e s can be o b t a i n e d . T h i s e f f e c t s h o u l d b e c o r r e l a t e d w i t h m o d i f i c a t i o n s o f t h e m i c r o s t r u c t u r e and changes of t h e microscopic mechanisms r e s p o n s i b l e f o r t h e r e l a x a t i o n . Moreover it i s e a s y t o u n d e r s t a n d why d i f f e r e n t a u t h o r s , s t u d y i n g a p p a r e n t l y t h e same r e l a x a t i o n mechanism measured q u i t e d i f f e r e n t r e l a x a t i o n p a r a m e t e r s . I t i s a l s o noteworthy t o o b s e r v e t h e v e r y i m p o r t a n t a m p l i t u d e dependence of t h e damping i n t h i s s t i l l low v i b r a t i o n amplitude range.

1000- 529K O e f . lo6 1 6 0 0 - 623K Def . 1 0 ~

n 2.5 + 2.5

+ 25 0 25

8 0 0 - ^t 1280 -

$ 9 6 0 -

0 6 0 0 - ⁺

++++

'd 4 0 0 -

'

^{6 4 0 -}

-

.P.+

_{- %be.,} ^{+++ -+++}

2 0 0 -

kt _%++++

^{3 2 0 -}

>'+*.;:mdilo-

%.++++!+

- 4 - 2 0 Log. N - 4 - 2 0 log. N

Fig. 1 Frequency s p e c t r a a t t h r e e d i f f e r e n t t e m p e r a t u r e s (491K, 529K, 633K) and two d i f f e r e n t amplitudes of v i b r a t i o n ( 2 . 5 . 1 0 - ~ and 2 . 5 .

- 2 -

:;

- 4 -6

1.5

1 0 0 0 / T

- Ln IN)

& - \ 5

\-i..

^{3+\0 ev}

- ^,

^{F i g . 2 .} Log f r e q u e n c y a s

a f u n c t i o n o f T - ~ f o r t h e peak of f i g . 1.

C8-302 JOURNAL DE PHYSIQUE

D e f . lo6

50

4 0 30 20

Fig. 3.

a-I

rob

- a

5

- I * *

$*

I%'f

-

-

^.Ix:

^<:- .

^*+

tt"t * * **:tt:.:,::.* 41..""2

x x l . l l x l

-

" S i g n a t u r e s " m e a s u r e d b) 1 2 t h c y c l e .

-10 0 10

D e f - lo6

a t 491K; VLF : H z . a ) 2 t h c y c l e ;

0 10

D e f . lo6

--

Fig. 4. I n f l u e n c e o f t h e t e m p e r a t u r e

-10 0 10

D e f . lo6 a ) 529K; b) 633K. VLF :

60 50.

4 0 - 30

Hz.

a-' loL

- a

P2

-

^{"+$ '}

ti " + r ^{X I+ +}

+. ' I x , X X * x ^{+ + + + *'+*'.} + ^{x + ' /}

-

-

-10 0 10

D e f . lo6

Fig. 5. I n f l u e n c e o f t h e VLF. a ) 5. H z ; b) Hz.

6 0 50 4 0 -

a-' . 10"

- b

11

-

/ x +

- ^{. =}

^Y

30-;>i2.++

+ , + . . * " +

*

-10 0 10

D e f . lo6

40-

35

30

25-

-

^{a-' . 104}

/

-

-

/+ /+

/+

l l , l , l , , , , l , L -4 - 3 -2

l o g N

F i g . 6 . I n t e r n a l f r i c t i o n measured a t GVLF = 0 a s a f u n c t i o n of t h e l o g f r e q u e n c y of t h e VLF v i b r a t i o n .

The measured s i g n a t u r e s a r e always observed u s i n g t h e same way ( f i g . 3 t o f i g . 5 ) . The specimen i s deformed by t o r s i o n a t d i f f e r e n t Very Low Frequency ( V L F ) : Hz, 5 . 1 O P 4 Hz and Hz. The a m p l i t u d e of t h i s VLF v i b r a t i o n i s 2 . 5 ~ 1 0 - ~ . During t h e s e VLF c y c l e s t h e damping i s measured u s i n g a h i g h e r frequency (15 Hz) superposed f o r c e d v i b r a t i o n . The a m p l i t u d e of t h i s v i b r a t i o n i s s m a l l e r ( 2 . 5 ~ 1 0 - 6 ) t h a n t h e VLF v i b r a t i o n . F i g . 3 shows t h a t t h e s i g n a t u r e does not depend s i g n i f i c a n t l y from t h e number of t h e VLF c y c l e .

The o b s e r v e d asymmetry i s o f s e c t i l e t y p e [ 1 , 3 1 . T h i s asymmetry d i s a p p e a r s a t h i g h e r t e m p e r a t u r e ( f i g

.

4 ) b u t r e a p p e a r s a f t e r lowering t h e t e m p e r a t u r e a g a i n . Except t h i s e f f e c t t h e g e n e r a l shape does not depend on t h e t e m p e r a t u r e o r on t h e f r e q u e n c y ( f i g . 5 ) . N e v e r t h e l e s s , t h e a m p l i t u d e o f t h e i n t e r n a l f r i c t i o n i n c r e a s e s w i t h t h e l o g a r i t h m of t h e frequency of t h e VLF v i b r a t i o n , a s shown i n f i g u r e 6 .

IV INTERPRETATION

The g o a l o f t h e s e f i r s t r e s u l t s i s e s s e n t i a l l y t o show t h e i n t e r e s t t o e x t r a p o l a t e t h e two waves a c o u s t i c method [ I ] i n d i f f e r e n t f r e q u e n c y r a n g e s . N e v e r t h e l e s s i t i s s t i l l d i f f i c u l t t o p r o p o s e a good i n t e r p r e t a t i o n of t h e r e s u l t s . The o b s e r v e d asymmetry was s u r p r i s i n g though t h e same t y p e of b e h a v i o u r h a s been a l r e a d y o b s e r v e d u s i n g t h e two waves a c o u s t i c method i n t h e t e m p e r a t u r e r a n g e o f t h e Bordoni r e l a x a t i o n [31. A s such an e f f e c t has been p r e v i o u s l y i n t e r p r e t e d by t h e e x i s t e n c e o f an i n t e r n a l s t r e s s f i e l d i n t h e s a m p l e , a s i m i l a r i n t e r p r e t a t i o n c o u l d b e p r o p o s e d i n o u r c a s e . Without i g n o r i n g t h e p o s s i b i l i t y o f an e x p e r i m e n t a l a r t e f a c t , t h e f a c t t h a t t h i s asymmetry d i s a p p e a r s a t h i g h e r t e m p e r a t u r e ( f i g . 4 ) means t h a t it s h o u l d b e c o r r e l a t e d t o a p h y s i c a l e f f e c t . The r e a p p e a r a n c e o f t h i s asymmetry a f t e r lowering t h e t e m p e r a t u r e a g a i n means t h a t t h e change is n o t due t o an a n n e a l i n g o f t h e sample, b u t t o a t e m p e r a t u r e dependance o f t h e mechanism which c o n t r o l s t h e d i s l o c a t i o n motion : t h e o b s t a c l e s which l i m i t t h e motion o f t h e d i s l o c a t i o n i n t h e low t e m p e r a t u r e r a n g e a r e no more a c t i v e a t h i g h e r t e m p e r a t u r e s .

A s t h e g e n e r a l s h a p e of t h e s i g n a t u r e i s f r e q u e n c y a n d t e m p e r a t u r e i n d e p e n d e n t , t h e r e s p o n s i b l e mechanism i s a p u r e h y s t e r e t i c o n e . Moreover t h i s shape i s v e r y s i m i l a r t o t h a t o b t a i n e d by C h i c o i s e t a l . [ 7 ] , when measuring u l t r a s o n i c a t t e n u a t i o n d u r i n g f a t i g u e t e s t , even i f t h e e x p e r i m e n t a l c o n d i t i o n s a r e q u i t e d i f f e r e n t . Such an e i g h t shape c u r v e c o u l d be i n t e r p r e t e d i n two ways : d r a g g i n g of a c l o u d o f mobile p o i n t d e f e c t s [ 9 ] o r i n t e r a c t i o n w i t h immobile o b s t a c l e s a s some i m p u r i t i e s o r t h e d i s l o c a t i o n f o r e s t [ 7 ] . The s e c t i l e t y p e o f t h e e i g h t shape c u r v e f a v o u r s t h e second i n t e r p r e t a t i o n . Moreover, t h i s mechanism seems n o t t o b e d i r e c t l y c o r r e i a t e d w i t h t h e r e l a x a t i o n peak observed i n f i g . 1 b u t s h o u l d b e c o r r e l a t e d w i t h t h e a m p l i t u d e dependence o f t h e damping.

The i n c r e a s e o f t h e damping w i t h t h e frequency of t h e VLF v i b r a t i o n has been q u i t e s y s t e m a t i c a l l y o b s e r v e d . T h i s i n c r e a s e c o u l d be c o r r e l a t e d w i t h t h e d e p i n n i n g o f t h e d i s l o c a t i o n s , i n d u c e d by t h e VLF v i b r a t i o n . But, it c o u l d a l s o b e due t o a c o u p l i n g between t h e h i g h f r e q u e n c y s t r e s s and t h e low frequency s t r a i n r a t e induced by t h e VLF s t r e s s . Such an i n c r e a s e o f t h e damping h a s been a l r e a d y o b s e r v e d d u r i n g p l a s t i c deformation [ 8 1

.

C8-304 JOURNAL DE PHYSIQUE

REFERENCES

1. G. Gremaud, M. Bujard, W. Benoit, J. Appl. Physics fi (1987) 1795.

2.

G.

Gremaud,

M.

Bujard,

J.

Phys. (Paris) (1985) C10-315.

3. M. Bujard, Thesis,

EPFL

(1985).

4. J. Woirgard,

J.

Phys. 42 (1981) C5-1135.

5.

T.S.

Ke, Phys. Review 11 (1947) 533.

6.

A.

Riviere, J.P. Amirault,

J.

Woirgard,

J.

Phys. 42 (1981) C5-439.

7. J. Chicois, R. Fougeres, G. Guichon, A. Hamel and A. Vincent, Acta Metall. 3 (1986) 2157.

8. J.L. Gacougnolle,

J.F.

Peltier and J. de Fouquet, Mechanical Testing for Deformation Model Development, ASTM STP 765, R.W. Rohde and J.C. Swearengen, eds., (1982) 67.

9.

G.

Gremaud, Li Ping Ho, W. Benoit, J. Phys. (Paris)

44

(1983) C9-581.